91Ó°ÊÓ

Show that for a quasistatic adiabatic process in a perfect gas, with constant specific heats, $$ \left(\gamma \equiv C_{p} / C_{y}\right) $$ $$ P V^{\prime}=\text { const. } $$

The molar energy of a monatomic gas which obeys van der Waals' equation is given by $$E=\frac{3}{2} R T-\frac{a}{V},$$ where \(V\) is the molar volume at temperature \(T\), and \(a\) is a constant. Initially one mole of the gas is at the temperature \(T_{1}\) and occupies a volume \(V_{1}\). The gas is allowed to expand adiabatically into a vacuum so that it occupies a total volume \(V_{2}\). What is the final temperature of the gas?

The enthalpy \(H\) is defined by \(H=E+P V\). Express the heat capacity at constant pressure in terms of \(H\).

One mole of a perfect gas performs a quasistatic cycle which consists of the following four successive stages: (i) from the state \(\left(P_{1}, V_{2}\right)\) at constant pressure to the state \(\left(P_{1}, \mathrm{~V}_{2}\right)\), (ii) at constant volume to the state \(\left(\mathrm{P}_{2}, \mathrm{~V}_{2}\right.\) ), (iii) at constant pressure to the state \(\left(P_{2}, V_{1}\right),(\mathrm{iV})\) at constant volume back to the initial state \(\left(\mathrm{P}_{2}, V_{I}\right)\). Find the work done on the gas in the cycle and the heat absorbed by the gas in the cycle.

Calculate the change in internal energy when 1 mole of liquid water at \(1 \mathrm{~atm}\) and \(100^{\circ} \mathrm{C}\) is evaporated to water vapour at the same pressure and temperature, given that the molar volumes of the liquid and the vapour under these conditions are \(18.8 \mathrm{cmVmol}\) and \(3.02 \times\) \(10^{4} \mathrm{~cm}^{3} / \mathrm{mol}\), and that the latent heat of evaporation is \(4.06 \times 10^{4}\) \(\mathrm{J} / \mathrm{mol}\).